Boosted top quarks in the ttbar dilepton channel:optimization of the lepton selection

DESY Summer School 2014

9 September, 2014

Author:Ibles Olcina Samblas*

Supervisor:Carmen Diez Pardos

Abstract

A study of boosted top quark topologies in tt events in thedilepton decay channels was performed with the data recordedin pp collisions at

√s = 8 TeV by the CMS detector during

the LHC 2012 run period, which corresponds to an integratedluminosity of 19.7 fb−1. The kinematics of the decay productsof boosted top quarks were studied and the criteria to selectthe leptons was optimized. The optimized selection leads to abetter agreement between Monte Carlo and data events, higherefficiency and a higher background rejection.

*Universitat de Valencia, Spain

Contents

1 Introduction 4

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2 ttbar production and decay products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Event selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Kinematics of boosted topologies 7

3 Optimization of lepton selection for boosted topologies 10

3.1 Standard isolation criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.2 2D cut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Results with the optimized selection 15

5 Conclusions 18

6 Acknowledgments 18

3

1 Introduction

1.1 Motivation

The top quark was discovered by the Tevatron experiments CDF and DØ in 1995, about 20 years after it hadbeen predicted. It is the heaviest elementary particle, with a mass of mt = 173.34±0.27 (stat.)±0.71 (syst.)GeV [1], which is of the same order of magnitude as the mass of a gold atom. Because of its huge mass, it is agood candidate for studies of the fermionic coupling to the Higgs boson. In addition, it has a lifetime whichis considerably shorter than the average time for hadronization, which causes that it always decays to otherfundamental particles before forming bound states. As a result, the top quark constitutes an importantfundamental particle for precision measurements of the Standard Model (SM) as well as for searches of newphysics beyond the SM. At the moment, the LHC can be regarded as a “top factory” since the large achievedluminosities results in large statistics of tt events.

The aim of this report is to outline the data analysis that was conducted within the top quark physicsgroup of CMS-DESY as part of the DESY summerschool 2014. The main goal of the analysis was to studytop quarks with very high momentum produced in pp collisions at the LHC and optimise the selection ofthe leptons produced in their decays. As part of the work, isolation efficiencies as well as trigger efficiencieswere studied (each term is explained later in the text) and an improved agreement between Monte Carloevents and data events was found. The data set used for this analysis is the one recorded in 2012 by theCMS detector at the LHC, which corresponds to pp collisions at

√s = 8 TeV and an integrated luminosity

of 19.7± 0.9 fb−1.

1.2 ttbar production and decay products

tt pairs of quarks are mainly produced through QCD processes. Such a pair of quarks can be produced fromeither a pair of gluons, Figure 1a, or a pair of quark and anti-quark, Figure 1b, being the first process thedominant one at the LHC. Once the top quark is produced, it decays in almost 100% of the cases to a W+

boson and a b quark (or the opposite charges for the t quark). According to the decay products of the Wboson, the tt events can be divided into three different categories (Figure 2):

� Fully hadronic channel: Both W bosons decay into a pair of quark and anti-quark of differentflavour. As a result, 6 quarks are produced in total. This channel has the largest branching fraction,about 44%, but also has a very high background coming from QCD processes.

� Semileptonic channel: One W boson decays to a pair of quark and anti-quark and the other toone charged lepton and a neutrino of the same flavour. As a result, 4 quarks, 1 charged lepton and1 neutrino are produced. The branching ratio of this channel is about 30% and it has a moderatebackground mainly coming from W production with additional jets (referred to as “W+jets”). Giventhe very short lifetime of the tau lepton, only electrons and muons are considered as possible leptoncandidates.

� Dilepton channel: Both W bosons decay into 1 charged lepton and 1 neutrino. As a result, 2 quarks,2 charged leptons and 2 neutrinos are produced. This channel has the lowest branching ratio, about5% but also has a very low background coming mainly from Z/γ∗− boson production with additionaljets (referred to as “Z+jets”) and QCD processes.

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(a) (b)

Figure 1: Leading order Feynman diagrams for strong production of top quark pairs from (a) quarks and (b)gluons. Source: DØ Collaboration.

(a) (b)

Figure 2: (a) Leading order Feynman diagram for the tt decay. (b) Top pair decay branching fractions. Source:DØ Collaboration.

1.3 Event selection

The dilepton channel was used for the analysis, which follows the same event selection and strategy as[3]. As a result, the relevant events for this analysis must contain 2 isolated, opposite-charged leptonswith high transverse momentum, since they are formed from a W boson, which is a very massive particle, 2energetic jets and large missing transverse energy, defined as ��E T = −

∑leptons

pT−∑jets

pT , due to the neutrinos.

Specifically, the requirements for the event selection are the following:

� Trigger: Events must pass first a trigger based on dileptons.

� Leptons: Electron candidates are required to have a transverse energy ET > 20 GeV and muoncandidates to have a transverse momentum pT > 20 GeV, within a pseudorapidity |η| < 2.4. Leptoncandidates are also required to fulfil an isolation criterion, which will be explained in Section 3.It is also required that mll > 20 GeV, where mll is the invariant mass of the selected lepton pair.Furthermore, most of the Z+jet background is removed for the µ+µ− and e+e− channels by rejectingevents in the Z0 mass region, which means rejecting events in the energy region 76 GeV < mll < 106GeV.

� b-jets: It is required to have at least two jets with pT > 30 GeV within a pseudorapidity |η| < 2.4. Ab-tagging algorithm is applied later to infer which of the jets came from a b quark. This is done using

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the property that B hadrons have a large decay length and therefore jets originated from a b quarktend to show displaced tracks or many secondary vertices. After updating the status of the selectedjets, only one b-tagged jet is required to avoid losing too many statistics.

� Missing transverse energy: It is required that ��E T > 40 GeV in the dimuon and dielectron channelsto reject a large fraction of background from “Z+jets” processes.

� Kinematic reconstruction: The kinematics of the full tt event can be totally reconstructed bysolving the kinematic equations, which are required to have at least one solution. The system ofequations is constructed using the four momenta of the 2 leptons, of the 2 jets and the missingtransverse energy. Then, the following assumptions are made to avoid having an unconstrained systemof equations:

– The missing transverse energy is entirely caused by the neutrinos.

– The lepton and the neutrino from the same top branch have an invariant mass equal to the Wmass, 84.4 GeV.

– The reconstructed top and anti-top quark masses are fixed to a nominal value of 172.5 GeV.

After applying these constrains, the system of equations can have up to 4 solutions. The ones withmore b-tagged jets and with the best reconstructed neutrino energy with respect to Monte Carlogenerated spectrum are preferred.

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2 Kinematics of boosted topologies

Figure 3a shows the distribution of the transverse momentum of the top quarks, which is obtained fromthe fully kinematic reconstruction of the tt system. To study the boosted regime, only top quarks with amomentum higher than 400 GeV are selected (“boosted tops” in the following), as can be seen in Figure 3b.Table 2 shows the comparison of the number of events and the signal to background ratio of the boostedand the not boosted regime. There is an excess of MC events over data events for the boosted regime, whichimplies a worse agreement between them. Also, the ratio of signal to background decreases. The main goalof this project was to improve the signal selection efficiency and the signal to background ratio for boostedtopologies by optimizing the event selection.

First, it was studied how the kinematic distributions of the decay products of the top quarks weremodified in the boosted regime. In Figure 4, the distribution of the angular distance between a lepton andthe corresponding b-jet, defined as ∆R ≡

√(∆η)2 + (∆φ)2, is represented for the full phase space and the

boosted region. In these two plots it can be observed that the distribution is shifted towards smaller angularvalues for the boosted region. This is expected, since the decay products of a top quark will be closer toeach other if the top quark has a high momentum.Figure 5 shows the distributions of the transverse momentum of the leptons and the b-jets as well as themissing transverse energy for the full phase space and the boosted region. In order to compare each pair ofdistributions better, the ratio between the tt signal in the boosted regime and the full phase space can beseen in the third column of Figure 5. It can be observed that a large fraction of leptons with high momentumare produced from boosted tops while this fraction is much lower for b-jets. Also, all the distributions inthe boosted regime show an excess of MC events, as already observed in Table 2.

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All data set Boosted regimeEvents Ratio over MC (%) Events Ratio over MC (%)

Total MC 64757 1023Total Data 64819 100.1 841 82.2

Total Background 14620 22.6 301 29.4tt signal 50137 77.4 722 70.6

Table 1: Total number of MC and data events as well as the fractions of tt signal and background for the full phasespace and the boosted regime for the combined dilepton channel. In the boosted regime, there is an excess of MCevents and the proportion of background events is larger than for the full phase space.

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3 Optimization of lepton selection for boosted topologies

In the previous section it was seen that the agreement between MC and data events was worse for boostedtopologies, as well as that the proportion of background events was larger. In this work, these statistics wereimproved by optimizing the selection of leptons in boosted topologies. Two optimizations were devised:

1. The first row of Figure 5 shows that almost half of the leptons in the boosted regime with pT < 40GeV comes from background events. Therefore, the cut on the transverse momentum of the leptonscould be changed from 20 to 40 GeV to reject a considerable amount of background. Furthermore,from the third plot of the first row it is observed that a very low fraction of boosted leptons would belost because of this new cut.

2. It was concluded from Figure 4 that the decay products of the top quarks are closer to each otherin the boosted regime. For this reason, the isolation criterion for boosted topologies for the leptonsshould be revised.

3.1 Standard isolation criterion

The standard isolation criterion used for the leptons is the following: accept event if IpfRel < 0.15 inside a

cone in η − φ space of ∆R < 0.3 around the lepton, where IpfRel is defined as:

I lrel =

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This means that the sum of transverse energy deposits from charged and neutral hadrons and photonsrelative to the transverse momentum of the lepton inside a certain cone around the lepton is small, so mostof the energy inside that cone comes from the lepton.

Figures 6a and 6b show the isolation efficiencies as a function of the transverse momentum of the topquarks and leptons, respectively, where the isolation efficiency is defined as the number of events that wererequired to fulfil an isolation condition by the total number of events. Figure 6a shows that the isolationefficiency is reasonably good for low momentum values of the top quarks but it decreases to values of almost50% for the highest momentum values. The opposite happens for the momentum of the leptons, as canbe seen in Figure 6b, where the worst efficiencies are obtained for the lowest values of the momentum.The decreased isolation efficiencies obtained with this isolation criterion motivated the search for anotherisolation criterion.

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3.2 2D cut

A new isolation criterion was studied, which will be referred as “2D cut”, states: accept the event is∆R(l, closest jet) > 0.5 or |prel

T (l, closest jet)| > 25 GeV, where prelT (l, closest jet) is the magnitude of

the transverse component of the momentum of the lepton relative to the momentum of its closest jet.

Consequently, events will be rejected if they do not satisfy both conditions at the same time. This is shownin Figure 7, where there are no events in the region of ∆R(l, closest jet) < 0.5 and |prel

T (l, closest jet)| < 25GeV. The comparison of the isolation efficiency between the two isolation conditions can be seen in Figure8 as a function of the transverse momentum of the top quarks, the leptons, the b-jets and the missingtransverse energy. The efficiencies obtained with the 2D cut shows a clear improvement in the boostedregion. Table 2 summarises the number of events lost and the efficiencies obtained with the full data setand the boosted regime. The isolation efficiencies are similar between the two isolation conditions for thefull data set, whereas the isolation efficiency of the 2D cut condition is 87.7%, about 15% higher that thestandard criterion for the boosted regime.

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Figure 7: 2D histogram to illustrate the working principle of the 2D cut condition. The x−axis is the ∆R betweena lepton and its closest jet and the y−axis is the magnitude of the transverse component of the lepton relative to themomentum of its closest jet.

No Isolation Cond. Regular Isolation Cond. 2D cut

All data sampleNumber of events 469277 444696 442814Loss of events 24581 26463Efficiency (%) 94.8 94.4

Boosted regimeNumber of events 7651 5595 6708Loss of events 2056 943Efficiency (%) 73.1 87.7

Table 2: Comparison of the total isolation efficiency between two different isolation criteria. The new criterion hasa 15% higher efficiency for the boosted regime.

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Figure 8: Comparison of isolation efficiencies for the two different isolation criteria as a function of the transversemomentum of the top quarks (top left), the leptons (top right), the b-jets (bottom left) and the missing transverseenergy (bottom right). The first plot is for the full data sample while the other three are for the boosted regime.

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Better isolation efficiencies are obtained with the new isolation condition. Nevertheless, given the impor-tance of the trigger in the selection of the leptons, trigger efficiencies with this new isolation condition werealso checked and compared to the ones obtained with the regular isolation condition. These efficiencies areshown in Figure 9 as a function of the transverse momentum of the top quarks, the leptons, the b-jets andthe missing transverse energy. In general, the trigger efficiencies with the 2D cut are about 4% lower, whichis a much smaller decrease compared to the gain in isolation efficiency.

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Figure 9: Comparison of trigger efficiencies for the two different isolation criteria as a function of the transversemomentum of the top quarks (top left), the leptons (top right), the b-jets (bottom left) and the missing transverseenergy (bottom right). The first plot is for the full data set while the other three are for the boosted regime.

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4 Results with the optimized selection

In this section, the new distributions using the two optimizations explained in the previous section areshown. Figure 10 shows the transverse momentum distribution of the top quarks for the full data set andthe boosted regime and in both cases a good agreement between MC and data events is observed. Table3 summarises the changes in the agreement between MC and data events as well as the proportions ofbackground and tt signal for each of the steps in the optimization process followed in this analysis. With thenew isolation condition, the efficiency is higher the agreement between MC and data events improves slightlyand it does not affect the fraction of background over signal obtained for the boosted regime. Changing alsothe cut in the transverse momentum of the leptons improves the agreement between MC and the proportionof background is much reduced. As a result, the optimized selection have similar proportions of backgroundand tt signal for the boosted regime to the ones of the original full data set, clearly better than the defaultselection.Figure 11 shows the fully optimized distributions of ∆R between a lepton and the corresponding b-jet, thetransverse momentum of the leptons and the b-jets as well as the missing transverse energy for the boostedregion in the eµ dilepton channel. All the distributions show a small excess of MC events over data events,as already seen in Table 3, but in general there is a clear improvement between them.

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Regular IC All data set Boosted regimeEvents Ratio over MC (%) Events Ratio over MC (%)

Total MC 38396 548Total Data 38239 99.6 472 86.2

Total Background 7708 20.1 157 28.7tt signal 30688 79.9 391 71.3

2D cut Boosted regime (20 GeV cut) Boosted regime (40 GeV cut)Events Ratio over MC (%) Events Ratio over MC (%)

Total MC 672 482Total Data 742 110.4 434 90.0

Total Background 204 30.3 106 22.1tt signal 468 69.7 376 77.9

Table 3: Total number of MC and data events as well as the fractions of tt signal and background for the regularisolation criterion (first table) and the 2D cut criterion (second table) for the eµ channel. With the new isolationcondition and the change of the cut to the transverse momentum of the leptons from 20 to 40, a similar proportionsof background and tt signal to the ones of the original full data set are obtained for the boosted regime (upper table,first column and lower table, second column).

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Figure 11: Distributions of some representative variables of the top decay products for the boosted regime andfor the eµ channel. From left to right and from top to bottom: ∆R between a lepton and the corresponding b-jet,transverse momentum of the leptons, b-jets and transverse missing energy.

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5 Conclusions

A study of top quarks with very high momentum was performed in the tt dilepton decay channels. Theconsequences of having boosted tops are that the distributions of the angular distance between a leptonand the corresponding b-jet were shifter towards smaller values, as well as the transverse momentum of thedecay products of the top quark took higher values. Applying the standard criteria to select the events,an excess of MC events over data events for the boosted regions and a higher proportion of backgroundevents was found. In order to improve the selection, two optimizations were studied. First, the cut on thetransverse momentum of the leptons was changed from 20 to 40 GeV to reject a larger fraction of backgroundwithout losing too many signal events in the boosted regime. Second, an alternative isolation criterion wasconsidered, which showed an improvement of approximately 15% in the isolation efficiency. The triggerefficiencies with the new isolation condition were about 4% worse than the standard isolation condition butthis is a much smaller decrease compared to the gain in isolation efficiency. With these improvements, therewas only an excess of the 10% of data over MC events. Furthermore, the proportion of background wasreduced considerably and it was similar to the one that in the full phase space.

6 Acknowledgments

I would like to thank Carmen Diez Pardos, the supervisor of this project, for her guidance and help duringthis summer programme. I found very interesting the work done together and I hope to have the chanceto collaborate with her again in the future. I am convinced that the experience gained here will help me inany future project that I undertake.I am also grateful to Ivan Asin, who kindly answered some of the many questions that I had the first weekshere and also gave me support and advice for my project. Finally, a special thanks goes to all the peoplethat makes this summer programme possible. I think that this is an incredible opportunity for any studentto extend his/her formation as a scientist.

References

[1] ATLAS, CDF, CMS and D0 Collaborations, First combination of Tevatron and LHC measurements ofthe top-quark mass, (2014). arXiv:1403.4427.

[2] CMS Collaboration, Measurement of differential top-quark pair production cross sections in pp collisionsat√

s = 7 TeV, EPJC 73 (2013) 2339. arXiv:1211.2220v3.

[3] CMS Collaboration, Measurement of differential top-quark pair production cross sections in pp collisionsat√

s = 8 TeV, (CMS PAS TOP-12-028).

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